A wireless network generally comprises of many smaller region called a cell that is further divided in to multiple sectors. Each cell/sector may have a base station (BS) and multiple mobile stations (MSs). The MSs in a sector may be fixed, nomadic or mobile. Communication from a BS to a MS is called as downlink or forward link. Similarly, communication from an MS to a BS is called as uplink or reverse link.
The radio frequency signal transmitted from the BS will travel through multiple paths before reaching the MS or vice versa. This results in the superposition of different multi-path signals, adding constructively and destructively at the receiver. The time varying nature of the mobile channel is due to the multipath time dispersion, doppler shift, and random phase modulation. Resolving the multipaths becomes difficult in system operating at very high carrier frequencies. The un-resolvable multiple paths contribute to fading and the resolvable multiple paths lead to inter-symbol interference (ISI). The presence of these resolved multipath components lead to the frequency selective nature of the wireless channel.
The problem of fading is overcome by providing multiple replicas of the transmitted signal to the receiver(s). This can be done by transmitting same (space-time coded) signals through all transmit antennas during the same time interval or at different time intervals to the receiver and/or by obtaining multiple replicas of the transmitted signal using multiple receivers. This is called as antenna diversity. This will ensure that less attenuated signal is available at the receiver under the assumption that the fading across the antennas are uncorrelated.
Cyclic delay diversity (CDD) is a scheme in which the cyclic shift of the first antenna is set to zero, while an antenna specific cyclic shift is applied to the remaining antennas. The cyclic shift is done after the N-point IFFT of the OFDM transmitter. The time domain CDD and the frequency domain phase diversity equivalent of a CDD signal is given by
            s      ⁡              (                  t          -                      δ                          n              T                                      )                    ︸              CDD        ⁢                                  ⁢        Signal              =            1              N              ⁢                  ∑        n                  N          -          1                    ⁢                          ⁢                                                  ⅇ                                                -                  j                                ⁢                                                      2                    ⁢                    π                                    N                                ⁢                                  nδ                  n                                                      ⁢            S            ⁢                          (              n              )                                            ︸            PhaseDiversitySignal                          ⁢                  ⅇ                                    -              j                        ⁢                                          2                ⁢                π                            N                        ⁢            nt                              
Where δnT is the antennas specific delay, N is the size of the IFFT. Note that in CDD the phase is varied on every subcarrier depending on the subcarrier index.
Space-time block coding (STBC) is a technique in which the signals to be transmitted will be coded across space (antennas) and time. When the encoding is done across space and frequency resource, it is called space-frequency block coding (SFBC). A STBC scheme with two transmit antennas is described below.
Signal s1 is transmitted through the first antenna and s2 is transmitted through the second antenna in time instant t and signal −s2* is transmitted through the first antenna and s1* is transmitted through the second antenna in next time instant t+T, where T is the symbol duration. The received signals r1 and r2 in two adjacent time instants is given by
      (                                        r            1                                                            r            2                                )    =                    (                                                            s                1                                                                    s                2                                                                                        -                                  s                  2                  *                                                                                    s                1                *                                                    )            ⁢              (                                                            h                1                                                                                        h                2                                                    )              +          (                                                  n              1                                                                          n              2                                          )      
After complex conjugating the received signal r2, the above equation can be written as
      (                                        r            1                                                            r            2            *                                )    =                    (                                                            h                1                                                                    h                2                                                                                        h                2                *                                                                    -                                  h                  1                  *                                                                    )            ⁢              (                                                            s                1                                                                                        s                2                                                    )              +          (                                                  n              1                                                                          n              2              *                                          )      
It can be easily shown that the channel matrix is orthogonal, and the receiver processing to detect s1 and s2 is linear. In case of SFBC, two frequency resources in one time instant are used instead of two time instants. The above scheme or its variant can be extended to arbitrary number of antennas.
Techniques like space-time block codes (STBC) and space frequency block codes (SFBC) have better performance as compared to CDD. In conventional STBC/SFBC schemes, distinct pilot tones are transmitted on different antennas which results in a high pilot overhead. STBC/SFBC schemes also require higher complexity during implementation. In ISI channels, the performance of Cyclic Delay Diversity (CDD) is generally poor. Phase diversity schemes are generally applicable to TDMA systems only. Phase diversity schemes are also restricted to one-dimension in time.